Question

The Rodriguez’s family drove from Tampa to Orlando during the summer. On the map Tampa is located at (-3,-5) and Orlando at (3,0). Find the coordinates of the rest stop that partitions the way in the ratio 1:4.

Answer 1

-1.8,-4

You're Welcome ;)) - Blake

Answer 2

The coordinates of the rest stop are
`(-(9)/(5),-4)`.

Explanation:

Given information: Tampa is located at (-3,-5) and Orlando at (3,0). The rest stop divides the way in the ratio 1:4.

Section formula:

If a line segments have two end points
`P(x_1,y_1)` and
`Q(x_2,y_2)` and a point divides the line PQ in m:n, then the coordinates of that point are

`((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))`

End points of the way are (-3,-5) and (3,0). Ratio is 1:4.

Using section formula we get

`(((1)(3)+(4)(-3))/(1+4),((1)(0)+(4)(-5))/(1+4))`

`((3-12)/(5),(0-20)/(5))`

`((-9)/(5),(-20)/(5))`

`(-(9)/(5),-4)`

Therefore the coordinates of the rest stop are
`(-(9)/(5),-4)`.